...and here's where I get stuck. Delta-epsilon proofs always seemed a bit circular to me, and what confuses me about proving "by contradiction" here is the fact that I should be able to choose some δ and the limit WOULD approach 1+10-10 :s... I'm a bit lost on where to go from here!

...and here's where I get stuck. Delta-epsilon proofs always seemed a bit circular to me, and what confuses me about proving "by contradiction" here is the fact that I should be able to choose some δ and the limit WOULD approach 1+10-10 :s... I'm a bit lost on where to go from here!

So the (sketch of a) proof would go something like this ...

Assume that the limit, L = 1+10-10.

Then pick ε small enough so that no matter how small δ is, it's impossible to find an x for which both of the following are true:

One half of that... so 0.5-10 (or 5-11)?
Did you choose this for some specific reason or just arbitrarily?

Another question -- If I'm choosing a specific value of ε here that isn't based on δ (so far as I can tell!), then do I still have to go through those initial steps of simplifying |f(x) - L | < ε to make the left-hand side look like the expression for delta (i.e., | x - 1| < δ )? Or am I missing the point of something here completely...

Hmm... Because to show that something isn't true, I just need one example that works to disprove it. So I really can just choose a small ε (like, an actual number that isn't in terms of δ) and show that it doesn't work once and that's it?

Hmm... Because to show that something isn't true, I just need one example that works to disprove it. So I really can just choose a small ε (like, an actual number that isn't in terms of δ) and show that it doesn't work once and that's it?